Preface of the book on Quantitative Aptitude for CAT

This is a copy of the preface from the book on quantitative aptitude for CAT. The book can be bought on Flipkart here .

The CAT is a wonderful exam because it aims to create challenging questions based on simple frameworks. In recent years, the paper has become far tougher, but examiners have ensured that the syllabus is simple. This is an often-forgotten, but key, idea that should set the tone for your preparation.

To my mind, this gives us two key guidelines

1. Learn from first principles to ensure that you do not ‘plateau’ out in some topics
2. Do not bother with really tough questions; do not agonize over speed of computation

To have a preparation strategy that keeps these aspects in mind, I have followed some simple thumb-rules. I have adhered to these rules while building content; my advice would be for students to stick to it as well.

Ø  Start from scratch (and then increase difficulty level slowly): The first few questions are beguilingly simple. The plan is to provide a framework for students to handle tougher questions. The most instructive way to learn is by discovering ideas. Every chapter is broken into theory, exercise and CAT-level questions. The idea is to provide a framework with simple questions and ‘push’ students to discover some thought processes while handling CAT-level questions.

Ø  Focus on building the thought process, and less on getting answers: Let me illustrate with a simple example. There is a rule that goes like this – For a prime p greater than 3, p² – 1 is always a multiple of 24. Many CAT aspirants might have seen this rule, but few might know the basis behind this rule. p² -1 = (p -1) (p + 1). Now, if p is a prime > 3, p is odd. p-1 and p+1 are consecutive even numbers, which implies one of them will be a multiple of 4 and the other a multiple of 2. Or, (p-1) (p +1) will be a multiple of 8. Now, p-1, p, p+1 are three consecutive integers, implying that one of these has to be a multiple of 3. p is prime; so one of p -1 or p + 1 has to be a multiple of 3. This is why, p² – 1 is a multiple of 24. If you have gone through this process and you see the next rule to be – If p is a prime > 3, p has to be of the form 6k + 1(where k is a  natural number), it becomes far easier to establish.

The entire book is built on the premise that it is the ability to figure out newer frameworks that distinguishes the best from the merely good, not a vast knowledge base that comprises many frameworks. Almost every question in the book has detailed solutions; in some answers, we revisit key bits from the theory in order to build the thought process.

Ø  Stay away from get-high-scores-quickly schemes: I have consciously stayed away from short-cuts and other over-simplifications to ensure a stubborn focus on fundamentals. Many guys who crack CAT will tell you that the exam is about speed and good time management.  They are correct. However, the ‘speed’ that they refer to is the ease with which you can zone in on the best method for a particular question, not necessarily the speed at which you can plug in a shortcut. I have appeared for the CAT multiple times and I can assert that if you ‘pick’ the best method as soon as you read the question, you’ll be able to approach all questions with time to spare. So, work on building that clarity. Many a time, this quest for speed is a distraction. If your fundamentals are sound, you will have time to burn.

Ø  Assess where you stand every now and then: Each topic ends with a set of CAT-level questions that acts as a benchmark for students. Innumerable books shoot either too low or too high when it comes to CAT preparation; I have taken enormous effort to ensure that CAT-level questions fall by and large into the band of difficulty that one is likely to encounter in the exam. If a student can confidently approach 80% of the questions in this category, he/she can be confident that this particular topic has been well covered. Barring the topic on combinatorics (where I have included a few tougher questions because learning by enumeration can be very instructive), almost every other question has been designed to be around the difficulty level one can expect in CAT.

I have made it a point to categorize questions into two levels of difficulty – Level 1 are questions that you should  see in a CAT paper; Level 2 are those that you should skip in the first round. I have limited the classification to two because when faced with a question in CAT, the only decision a student has to take is ‘now or later?’.  It is that simple. Also, to aid this decision-making, I have made it a point to provide the level of difficulty only in the solutions section, thus giving students practice in this decision-making.

Ø  Prepare with intensity, but enjoy the process: CAT tests intensity and stamina as much as it does application. Completing a 140-minute exam without concentration ‘drops’ is not easy. It takes immense practice. So, set yourself targets of 20 or 25 minutes for intense preparation and build up from there. Contrary to popular perception, this is not an exam that one should prepare for eight hours a day. If you study with intensity, it is difficult to spend more than two-three hours a day on CAT preparation. And, if you can do two hours a day with intensity for 90- 100 days, you will be in great shape for the exam. Focus on intensity, not time. Intensity can be built up without a feeling of being burdened by it only if you enjoy this process at some level. Looked at differently, CAT preparation can be seen as being similar to solving Sudoku or math puzzles along with some general reading. If your attitude is correct, this can be a lot of fun.

What does the book provide?

There are 27 chapters in math, with each topic containing theory with solved examples, exercise questions and CAT-level questions. All questions have detailed solutions. The level of difficulty of the CAT-level questions is mentioned where solutions are provided. This is supplemented with CAT papers of 2006, 2007 and 2008 (with solutions provided for the first two). There are also three mock CAT papers for the Quant section, again with solutions provided for the first two.

I enjoyed creating the content for this book. Although a fairly arduous task, what started off as just another interesting project soon became a labor of love. I have a lot of fun when I am in a class or when interacting with students. I realized that my maiden venture as an author for a publishing house was also very enjoyable! It is my hope and expectation that students will find it useful and also fun. Mathematics is best understood when learnt with a certain sense of wonder and joy.

Finally, to the caveat emptor – notwithstanding the meticulous efforts undertaken by the team in putting together this book, it is possible that a few errors have crept in. Kindly bring it to our notice in case you notice any. This will help us improve our next edition. I can be reached at rajesh@2iim.com

What does the book not provide?

I have always believed that it is crucial to know what is not in any book. This book provides a good framework and detailed thought process for a number of challenging questions. However, the book does not provide what I would call “The Grind”.

Students are expected to know the simple basics of the topics being covered.  In case you feel like a particular topic is too complex, please look into NCERT class VI, VII or VIII text books and get an understanding of the fundamentals.

While learning some topics, we are more receptive of tougher ideas after we have internalized the simpler ones well and practiced plenty of questions on these. The pace of learning is determined by the amount of “Grind” required to be receptive to the next idea. As my mentor K S Baskar never tires of saying, each person should do the level of “Grind” required for him/her (and not get carried away with doing only as many as the best student in your peer group requires). So, if you feel like you require more practice of simpler questions before going to CAT-level questions, please suspend pride and pick up the NCERT class VI, VII or VIII books and have a go at them.

Best wishes for the CAT and other competitive exams.

Acknowledgement

I would like to convey my sincere thanks to my colleagues, who painstakingly reviewed most of the content. Special thanks are due to Shivaram (faculty at 2iim Chennai who is now off to IIM-A for his PGDM); Naveenan Ramachandran (IIM-A alumnus, who runs 2iim Mumbai); Vimal Gopinath (XIMB alumnus, who runs 2iim Bangalore); K.S. Baskar (IIMC alumnus, who is the founder of 2iim);  Naveen (quant faculty at 2iim Chennai); and Mr. G R K Murthy (IIT Kanpur alumnus, who runs 2iim at Mylapore, Chennai).

I am grateful to Ranjini for her enormous help in formatting and verifying content. I am thankful to Mr. Periyathambi Srinivasan for ensuring that our office functioned smoothly enough when we were wholly occupied with the book.

I also acknowledge the contribution of Mr. Biju Kumar and his entire team at Access Publishing for the editing, proof-checking and general guidance they have provided. This has been invaluable.

Finally, I am indebted to Ms. Ranjeetha Shivakumar (alumnus of Great Lakes, Chennai) for verifying parts of the content. As the author’s better half, Ranjeetha had the unenviable task of having to get her hands dirty with what was not really in her comfort zone.

Three step process for CAT Quant preparation

The below is an extract from the article published on MBA Universe that can be found here

For each topic in Quant section, you must break the process into three steps - 

 1. Learn the theory from first principles: Make a conscious effort to learn theory from basic ideas. We have a tendency to ‘jump’ steps when we get familiar with a topic. Resist the temptation to use plug-and-play formulae and learn the theory with an open mind. Let me illustrate this with a simple example – 

Consider a class of 40 students with an average score of 60 marks. Two students leave this class and the average mark increases by ‘x’. If no student can take a negative mark, and x is a positive integer, how many values can the average of the two students take? One can write equations and solve this. However, someone who has learnt from basic ideas will follow a more intuitive approach.

Let us look at this approach. Let us start with a simple case where the average does not change when these two students leave the class. In this case, the two students should have scored 120 marks overall (average of 60). Now, since the average has increased, these two together should have scored less than 120.

If the average increases by 1, then they should have scored 38 marks less than 120. If average increases by 1, total should have increased by 38, or the two that left the class should have ‘taken out’ 38 less than 120. So, if they had scored 120 – 38 = 82, the average would have fallen by 1.

If they had scored 120 - 38 x 2 = 44, average would fall by 2. If they had scored 120 – 38 x 3 = 6, average would have fallen by 3. Three different possibilities exist. The intuitive method scores over the formulaic method in questions like these. It is very important to retain the more intuitive approach and not get consumed by the algebra .........more

What should you make right this CAT vis-a-vis your last CAT?

Category I: I am a rockstar in one of the two sections but have no idea whatsoever about the other.

Kudos! You have identified your strength.  Now, play to your strength.  If your strong area is, say, Section I i.e., Quant and DI, never even shoot to attempt (and get right) less than 26 questions.  Make this a habit right from your first mock.  Remember, this means you don't have the freedom of either focusing less on DI because you don't like calculations (Hi five! I am one among them) or focusing less on a particular chapter, like say Work and Time, because you don't deem it important/don't like it.  Doing this would ensure a 99.6x+ percentile in this section. Believe me, the gap between a 99.6 and a 98.5 percentile is wider than you think because the gap in the CAT score out of 450 could be much higher than the percentile difference suggests.  Since the interview call is based on the CAT score out of 450, the percentile number could be slightly misleading.

Fine. Got it. But, what do I do about the other section?

If you are a rock-star in Section I, then it is almost impossible that you don't understand anything of LR in Section II. Well then, that's your strength in Section II. I know of candidates who attempted just the 9 or 10 LR questions in Section II, ended up scoring an 80.xx percentile but maxed Section I by scoring a 99.9x and landed a seat with a top IIM. That's a smart strategy. But be cautious about the cut-offs for general/OBC/SC/ST categories. Of course, not many people would want to do this and you don't have to either. Anyone who is a rock-star in one section and has no idea about the other has just not tried enough. A person's skill sets for these two sections are not so poorly correlated, after all. Reading Comprehension is, by far, the best sub-section in Verbal that one can focus on. You know you would get around nine or 10 questions of RC and any candidate with a decent understanding of English (if you can max out Section I, you got to be decent in English) can attempt and get right four or five questions. While you are practicing RCs, do not focus on building speed. Focus on understanding what you read. Not being able to attempt enough questions is primarily a function of being unable to correctly answer a question in the first attempt; this happens because you can't understand the question. With this, you might be able to increase the count of RC questions to seven or eight. So, nine or ten LR questions plus seven or eight RC questions and you already have 16-18 correct attempts in your kitty. With a good understanding of passages, you will begin to get most of the answers in Sentence Rearrangement and Paragraph Completion/Elimination questions right. That's three or four questions more. A total of 20 to 22 correct attempts in your weaker section is brilliant. Again, this is something you should practice right from your early mocks.

Category II:  I am not a rock-star in either of the two sections but I almost always manage to get a balanced score.

Well, this is tricky. I know it is because I am one of your kinds. You always have this feeling that you are almost there, yet far. I have come to realize that being able to get a balanced score is actually not that bad. If you also know that you would always score in the range of 94.xx to 98.xx percentile in both sections with an overall of 97.xx to 98.xx, you should focus on accuracy in attempts. Only accuracy can take you from 98.xx to 99.7x and is important for any candidate (especially in the open category and with not-so-decent academics) to secure an interview call from at least a few IIMs. You know you are going to be capped at 22-23 question attempts in each of the sections and you cannot afford to get even a single one wrong.  And for that level of accuracy, besides the fact that you should read every question properly and not fall for common traps, you should not get anxious in the examination hall. Calm down your nerves before you hit Start.

Calm down my nerves!?! That's easier said than done.

True. There's no one way to do this. Even the most careless of all test-takers will have a moment of anxiety while entering the exam hall. However, there's one thing you might consider doing. I did this but I can't say for sure if it worked or not. Do not write only the CAT and be hell bent on joining only the top IIMs.  Broaden your options. There are so many other good B-schools in India, including FMS, XLRI, MDI, IIFT and the likes. If you are prepared for the CAT, you are prepared for pretty much any other exam. So write XAT and IIFT, for sure. You might want to add NMAT and SNAP too. Also, apply well in advance to B-schools that accept CAT/XAT scores such as SP Jain, MDI and FMS. Two reasons why this might help: One, if some of these exams were to happen before CAT, that's good exam-day practice. Two, by applying to so many B-schools, you end up knowing a lot of information about them, thereby realizing that you do have a larger basket of 'good' options to choose from. For all you know, you might end up with a BCG offer from FMS/XLRI than if you had been to IIM-A/B/C!

The author of the above piece is Shivaram, a graduate from College of Engineering at Guindy in Chennai, Class of 2010. He worked with 2IIM for a year before joining IIM-A in 2012. 

Common traps to avoid in the Quant section

For most candidates, Quantitative Aptitude is probably the most challenging section to crack in the CAT.  During your preparation, or at least during your full length test-practise stage, you would have developed an idea of what your strongest and weakest areas are (if you haven't, do it at the earliest! It is important to know your strengths as well as your weaknesses.).

The reasons why Quant can be the toughest nut to crack are varied. Most students have a sufficiently good grasp of fundamentals. But, when a challenging question presents itself, they are all at sea. Most students also have a problem with time management. Some would have lost touch with Quant basics after high school. Some don't have the raw speed of formulation and calculation that most “math whizzes” take for granted. Whatever be your tale of woe, remember that that whole point of the CAT preparation exercise is to understand what your weakness is, and work towards improving it.

In the following pages, a few common traps and pitfalls are detailed. Beware of these on the day of the exam. But don't fall into the trap of assuming that these tips have only to be glanced over once before exam day. You may need to go through these in the test practise stage (and possibly even during the preparation stage), so that you can identify and rectify your “favourite” mistake area.

Common pitfalls in the Quant section

1. Problem vs You

The test makers of CAT are experienced in the art of mixing up easy and difficult questions. When you take the CAT, you will find that there are a few absolutely easy questions that you could have solved when you were in 7^th standard. You will also find questions that are extremely tough. This is not done to identify and select the math majors! The reason there is a mixture of questions of varying levels of difficulty is that it reflects real life situations. But, given that you have a deadline, you have to pick and target the lowest hanging fruits.

The CAT will definitely contain difficult problems, and there are good chances that you might start solving them and get stuck somewhere, only to realise eight minutes or so later that you aren't making any headway. So what should you do? Leave it right there and move on to the next question. But what do you do instead? Spend another three minutes just to try to solve the problem and show it who the boss is!

This is probably the most common trap – getting into a literal “fight” with the problem, where solving one problem becomes more important than getting a good sectional score overall. This is a definite way of losing good time that can be employed productively elsewhere.

So how do you avoid this trap? First of all, be aware of it when it happens. When you realise that you have spent more than reasonable time on a question and you are still nowhere close to finding an answer, it is time to consider moving on. How do you know that you are falling into this trap? 

Here are some indicators that might help you decide:

• Your equations begin to get bigger and uglier
• You have filled up half the rough-sheet and have made no real progress
• None of the answer substitution or elimination tricks appears to work
• You go back to reading the question several times
• You see the clock ticking, and you realise that you still haven't even attempted a majority of the section.
• Most of all, you have spent five minutes on this question already and you are still where you started.

What do you do in such a situation? Do you panic and give up? Doing so is going to give you a sense of failure, which will not only affect the rest of your Quant section, but also likely spill over into the Verbal section. At the same time, you can't continue spending time on the same question.

The best way to deal with this situation is to not let it arise in the first place. Make sure that you pick the easy questions first and dispatch them. Then, move on to the marked questions which you think can be solved with some effort. Finally, only when every easy or medium-difficult question is attempted, should you even consider taking up questions from areas you are not comfortable with. 

Remain calm throughout the section.

If you do find yourself in such a situation, identify early when to give up and move on to the next question. Your ego might hurt a bit, but it is definitely not worse than leaving questions unattempted towards the end.

2. Knowing a formula is not the same as Understanding a concept

A lot of students, especially in the later stages of preparation, say that they know all concepts very well, but when it comes to solving problems, they get stuck in the question interpretation or the formulation stage. For example, you “know” what the modulus of a number is. You have read and memorised all the definitions, and you even remember the textbook example well. You also know how to solve each equation type, and yet when you see an equation such as the following one, you get stumped:

|2x – 5| > 2

Now, ask yourself this: If you know all the formulae, theorems and definitions in a particular topic, does it mean that you really “understand” the topic? “Understanding” doesn't mean being able to reproduce or replicate a stated theorem or a solved example. You understand a concept when you are able to visualise it and, and then use your creativity to formulate and obtain a non-mathematical model of something as “dry” as a modulus equation, for example. In this instant case,  |a – b| would mean the distance from the point “a” to the point “b” on the number line. So the distance from the point “2x” and the point “5” is more than 2 units. Or, “2x” is either greater than 7, or less than 3. Aim to achieve a good visual parallel for as many concepts as possible. This not only saves time in solutions, but also gives you clarity of thought.

This is a trap students often fall into. Math problems on the CAT test more than your memory. They test how well you can adapt to situations, and apply simple concepts in complex problems. Be aware of this from an early stage in preparation. Spend more time on the basics. If you have trouble understanding a concept at first, reflect on it till it makes sense. This is more important than solving a dozen questions based just on formula application.

3. Poor time management

Another trap that most test takers fall into is lack of proper time management. Given that there are only 30 questions in a section, and more than two lakh students write the CAT, the difference between an extremely high and a low percentile could be a matter of just one question. You need to make sure that you have at least seen and attempted all the questions in each section, lest you should leave out easy questions towards the end. This calls for a lot of practise. Do as many full length practise tests as possible, and get used to the rigour of a full-length test. You need to sustain your concentration for the entire duration of the test, and you need to have the endurance to finish the test with almost the same energy and alertness as when you started.

Do not leave too many questions to the end. Doing so will only make you more nervous, and you may lose out on some really easy questions.

4. Improper reading of the question

Sometimes you solve an entire question correctly only to find out that you had made a mistake in reading the question. Even though you did everything right, your answer was wrong. Such errors in reading or interpretation show a lack of focus in the early part of solution.

• You may have to slow down while reading the question, and maybe even read it twice to understand it completely. Do not try to save time in this stage!
• Pay special attention to words and phrases in the question whose incorrect interpretation may change the answer drastically. Some examples of such words are:

◦     Distinct, Integer, Positive / Negative / Non-negative, At least / At most, Odds in favour / Odds against, Some / All, And / Or, Not less than / Never greater than

• Also after solving the question, you can verify your answer by re-checking it with the scenario presented in the question. You may not always have time during the test to double-check every solution, but if you have a serious doubt, you can always exercise this option.
• After getting the answer, read the question again because it may ask you to process the solution before arriving at the answer. For example, you may have solved an equation for x, but the question may ask you to find the value of x + 10. Re-read the question to be sure.

6. Silly errors

This is probably the most frustrating of them all. Everything about your solution was correct, except  that you made a silly addition mistake in the final step, and you lost everything because of that. Errors in calculation or solution happen to the best of us, and it is never good when it happens.

Can you improve your accuracy and reduce the number of silly mistakes? Absolutely, yes. Just slow down while solving equations, or be a bit more careful with calculations. Also, practise a lot. Learn the multiplication tables and ratio charts. Do the grind. All that is good enough preparation. But will that help you completely eliminate calculation errors? Unlikely.

Humans are prone to making errors in calculations. You cannot completely eliminate calculation or solution errors. But you can definitely improve your accuracy and reduce the time you take for calculations.

Here is what you can do:

• Find out your strongest and weakest areas. Figure out where you need improvement the most? Is it multiplication tables? Is it quadratic equation solutions?
• Work hard on improving your speed and accuracy in those areas. Keep working on it on a daily basis. You will definitely see an improvement in performance.
• Practise, Practise, Practise.
• On the day of the test, accept that you may still make mistakes. Allow for a margin of error, but be extra careful in areas where you know that you have a proven weakness. If possible, double-check your answers by working backwards from the answer options.

All these things are easier said than done, and it is always easier to rely on hindsight and compile a list than it is to log your errors and rigorously practise on a daily basis. But do remember that whatever your starting point is, you can always, always improve. And whatever be your level of preparation, a bit of caution on the day of the test will definitely pay large dividends.

7.  Build your Eye for detail

Relentlessly train yourself to pick anomalies. If you did not notice, we have jumped from point 4 to point 6 on this list! Every time you let something like this pass you by, make a mental note to look or detail. Just becoming more ‘switched on’ makes a big difference and can be built with practise.

The above article was contributed by Vimal Gopinath, an XIM Bhubaneshwar alumnus who runs 2IIM Bengaluru. The article also features in the CAT Quant book authored by Rajesh Balasubramanian.   

Under what circumstances is it a good idea to quit your job and prepare for CAT?

Under what circumstances is it a good idea to quit your job and prepare for CAT?

NONE!

This is one of those essay topics that can ideally feature in competitions seeking ultra-short contributions. The one-word response would be, ‘None’!  However, having told my boss that I definitely want to comment on this topic, I cannot get away with the ultra-short version. So, here goes.

Thanks to my earlier avatar as an investment research analyst, I have acquired this habit of getting my disclaimers in early. I am not going to sit on the fence. It is NEVER a good idea to quit your job. So, if you are among the group of people that has decided to quit and you do not want to hear anything against that decision, skip this article and move ahead to the next one.

Every week, I get at least two enquiries from students who are keen to take a step up by focusing exclusively on the CAT preparation. This roughly translates to, “I hate my job.  I want to have a decent-sounding reason to quit”. Beware! there are two major pitfalls in quitting a job to prepare for CAT.

1. The personal interview phase becomes trickier: You will lose scores for work experience, and might face uncomfortable questions in the interview. Sample this
1. “Quitting a job at an MNC to prepare for CAT makes me doubt your ability to weigh risk-reward.  I think I would be fueling your foolhardy decision-making if I gave you a seat here.  What are your thoughts on this?”
2. “I met eight candidates before you, all of whom have managed busy work schedules and squeezed in CAT preparation while you have focused exclusively on CAT. All other things being equal, why should I select you over them?”
3. “So, you cannot hold a job and prepare for a competitive exam at the same time?  After MBA, you will have to multitask at an even greater level.  You are basically telling me you are not equipped to handle that.  Thoughts?”

Do not think that it is a smart idea to say that you have not quit your job but taken a break to pursue your passion of working in industry X and therefore joined your cousin.

As a general rule, professors do not think it is a great idea to take a break for the sake of CAT preparation and will interpret any shift to a ‘small company in a preferred industry’ on your resume as a proxy for this.

2. Pressure increases: Bear in mind that if you take a break in June, you do not take a six-month break for CAT preparation, but rather a nearly 12-month break.  CAT is not an exam that one needs to prepare for 50 hours a week; it calls for intensity over two-three hours a day.  A longer preparation time could easily lead to a plateau in results performance.  A large number of candidates run out of practice material that really tests them but can never cross 90^th percentile. This is essentially because the intensity disappears from preparation.  If you set yourself a target of preparing for eight hours a day for 180 days, you are creating a recipe for losing intensity within weeks.  All these factors will intensify the pressure on the day of the exam.  Importantly, this plays a role in affecting decision-making after CAT as well.  If you do not have a viable plan B, the temptation to join a college ranked 60^th (because this is the only decent admit) will be high. The assurance that comes with having a viable plan B is vital for cracking this exam.

There are many other reasons for not taking this decision, but the two mentioned above are the most important.

Compared to 10 years ago, the admission processes for the IIMs have changed dramatically. When I took my CAT in 2000, the admission process was extremely CAT score oriented. If you had a decent CAT score, all else was pretty much forgotten (particularly true for IIMC).  In the current era, the CAT score is taken as but one metric in a broad basket of input variables. Ten years ago, it might have been a decent (if still risky) idea to trade 2 percentile points for one year of work experience.  In the current era, the trade-off is not even worth the discussion.

Do not try to use CAT as an excuse for getting out of a taxing/boring job.  Even after your MBA, odds are that you will go through a few bad jobs (and bosses!)  If you must quit, do so in August, have a job in hand that you plan to join by Nov 1^st.  Take a six-to-eight-week break, have a go at CAT in this time window and hope for the best.